Problem: Solve for $z$, $ \dfrac{10}{8z^2} = \dfrac{z - 3}{8z^2} + \dfrac{10}{16z^2} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $8z^2$ $8z^2$ and $16z^2$ The common denominator is $16z^2$ To get $16z^2$ in the denominator of the first term, multiply it by $\frac{2}{2}$ $ \dfrac{10}{8z^2} \times \dfrac{2}{2} = \dfrac{20}{16z^2} $ To get $16z^2$ in the denominator of the second term, multiply it by $\frac{2}{2}$ $ \dfrac{z - 3}{8z^2} \times \dfrac{2}{2} = \dfrac{2z - 6}{16z^2} $ The denominator of the third term is already $16z^2$ , so we don't need to change it. This give us: $ \dfrac{20}{16z^2} = \dfrac{2z - 6}{16z^2} + \dfrac{10}{16z^2} $ If we multiply both sides of the equation by $16z^2$ , we get: $ 20 = 2z - 6 + 10$ $ 20 = 2z + 4$ $ 16 = 2z $ $ z = 8$